Corrupted? Plane with White material rendering Black in Solid view
The problem is you need to apply your scale transforms on the objects. The reason the faces are shading poorly is because of Z-fighting, which is occurring because your objects have zero Z scale value. Applying scale will also allow your modifiers to work. 

To apply the scale, select all your objects in object mode, press Ctrl-A and Scale. Or in the viewport header, Object -> Apply -> Scale

Your scale values should now read 1.0, 1.0, 1.0.